Why does the equivalence point occur at different pH values for the four titration studied?

the four titrations were:
1. HCL with NaOH
2.HC2H3O2 with NaOH
3. HCl with NH4OH
4. HC2H3O2 with NHOH

Okay so equivalence point is when the number of moles of acids and bases are equal. So why does it have different pH values at equivalence point, because if there are more base species then the pH will be higher and if there are more acid then it would be lower?

Strong acid/strong base is SA/SB.

Strong acid/weak base is SA/WB.
Weak acid/strong bse is WA/SB.
Weak acid/weak base is WA/WB.

The simple answer is that the salt formed at the equivalence may or may not hydrolyze. Each scenario is discussed below.

#1.
What is the salt in #1 of your question. NaCl. Will either Na^+ or Cl^- react with water? No. So NaCl in solution at the equivalece point is just pure water and you know the pH of pure water is (H^+) = (OH^-) and pH = 7.0

#2.
What is the salt for the second example? At the equivalence point you will have NaC2H3O2 (sodium acetate). Will either react with water? Na, no. Acetate, yes. You've written these I know.
C2H3O2^- + HOH ==> HC2H3O2 + OH^-
When I was in school they called this a hydrolysis reaction. It has a constant. Today they talk about the acetate ion, the C2H3O2^- being a stronger base than water. So it pulls a H away from water, to form the weak acid, HC2H3O2, but notice that OH^- is liberated. And what does extra OH^- in solution mean? It means the solution is basic. Right? So the pH of a WA/SB titration is in the neighborhood of 8-9.

#3.
What about the salt for #3. That would be NH4Cl. Will NH4^ or Cl^- hydrolyze? Cl^- no. NH4^+ yes. In modern day work, then the NH4^+ is a stronger acid than H2O, therefore, it donates a proton to H2O. In my day it was hydrolyzed. It has a constant.
NH4^+ + HOH ==> NH3 + H3O^+.
The main idea here, of course, is that H3O^+ is liberated. And if we add H3O^+ to neutral water, we end up with an acid solution, don't we? So SA/WB titrations end up with a pH in the neighborhood of 4-5.

#4. Technically, you can't titrate a weak acid/weak base. Practically, it isn't possible either. In this case, since both acetic acid and NH4OH have about the same Ka (or Kb), then the NH4C2H3O2 is about neutral. And the equivalence point may move slightly acid, to neutral, to slightly basic, depending upon Ka and Kb of the acid/base system.

You will remember that you used different indicators? Why did you do that? Because you want the indicator to change at the same pH as the equivalence point. Therefore, you used one kind of indicator for #1, another for #2 and another for #3.

whoa ummm we only used one indicator phenolphthalein in fact the question also asks for which trials that the indicator we used as a good one and for which it was poor. i came to the conclusion that it was good for the first two which was HCl and NaOH and HC2H3O2 since at least the endpoint for both of these were slightly under the equivalence point but was somewhere somewhat close to the rapid pH increase. The first one was a little bit before the increase began though. Then trials 3 and 4 with HCl and NH4OH and actic acid and NH4OH needed a different indicator because trial 3 didn't even really change colors and trial 4's change came after the rapid increase.

Phenolphthalein changes color at 8-10 which is just right for WA/SB and it works very well for SA/SB, too, because the vertical rise for SA/SB for say 0.1 M acid with 0.1 M base, starts about 4 or so and goes almost straight up to about pH 9.5 or 10. So the titration error using phenolphthalein with this titration is so small it's negligible. But you CAN NOT use phenolphthalein for the SA/WB, which you just said, and for that reason. The indicator changes color around 9 and the end point is around 5. I say you can't use it; technically, you CAN but the error will be significant. The trial 4 change (WA/WB) has no sharp end point.

so was i somewhat right? I have to write this for a lab report that's why

You are exactly right on SA/SB and WA/SB.

I can't comment on trial 3 and trial 4 since I don't know what your curves look like. I would just write what happened. From my perspective, there is no sharp change for wa/wb but the computer can be programmed to give any kinf of a curve desired.

Why does the equivalence point occur at different pH value for the four titrations studied? ( Hint: what species are present at the equivalence point for each trial)

So the answer would be that it occurs at different pH values because equivalence point for those with higher acid will be low and ph for those with higher base will be high.

Is the salt that you're talking about the "species" that are present at the equivalence point of each trail that the "hint" is referring to?

also how do we determine whether or not an indicator is the good one to use for a trial? I know that phenolphthalein turns to pink 8.3-10.0 pH so that means that it's good for the equivalence points in between those?

Generally, yes. When I talk about salt, that is a generic term. For your HCl/NaOH it is NaCl but thre "species" will be Na^+ and Cl^-.

For acetic acid/NaOH, the salt is sodium acetate but the species are Na^+ and C2H3O2^-.
For the NH4OH/HCl, the salt is NH4Cl but the species are NH^+ and Cl^-.

As for your explanation about higher acid and higher base, I don't know what you mean by higher. I would answer that the pH is higher than 7 when the anion (the specie) is a stronger base than water and it is lower than 7 when the cation is a stronger acid than water. (This is all about the Bronsted theory of acid/bases).

That's right. Or it also may be used (for example in the HCl/NaOH titration) if the vertical portion of the curve is so steep that the equivalence point and the end point are essentially the same.

ok goodnight I'll talk to you tomorrow. Thank you again!